I have several subsites and all are consuming the Parent Site content types for metadata applied to lists and libraries. However one of the sites need to break Site inheritance for content security purposes to retain access to a selected set of users. If the child site breaks Site inheritance from the parent site, will the content type connection still be retained between parent and child site?
Permission inheritance, and the breaking of inheritance, is in the realm of user access. A user authenticates herself to the environment, usually Active Directory, which verifies that the user is authentic. The user proves to the system that the user really is the one she claims (pun intended) to be.
So now the system knows who she is. The next step is authorization, where a user is part of a AD security group often given authorization through a SharePoint group. Let's say domain/allUsers is put in the SharePoint group Visitors, and the Visitor group is added to your site. The Visitor group have read permission to the site. This means that all users now have read permission to your site. All users are authorized to visit the site once they have authenticated themselves.
On a subsite, where you break inheritance, and remove the Visitor group - you are actually removing authorization for all users to visit the subsite. The users are still authorized to access the main site, but not the subsite.
All of this have nothing to do with content types, which don't have permissions, authentication or authorization. Breaking permission, and removing groups doesn't effect content type inheritance.
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